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Ordered quantization and the Ehrenfest time scale.

R M Angelo1, L Sanz, K Furuya

  • 1Instituto de Física Gleb Wataghin, CP 6165, Universidade Estadual de Campinas, Unicamp 13083-970, Campinas, São Paulo, Brazil.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|August 26, 2003
PubMed
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We introduce a novel quantization method for classical monomials in bosonic theories. This approach enables calculation of quantum expectation values and provides a general expression for the Ehrenfest time.

Area of Science:

  • Quantum mechanics
  • Quantum optics
  • Mathematical physics

Background:

  • Classical monomials and their quantization present challenges in bosonic theories.
  • Understanding quantum expectation values and semiclassical expansions is crucial for theoretical physics.

Purpose of the Study:

  • To propose a prescription for quantizing classical monomials using noncommuting operators.
  • To apply these rules to quantize a time-evolved function and calculate its expectation value in coherent states.
  • To derive a general expression for the Ehrenfest time.

Main Methods:

  • Symmetric and ordered expansions of noncommuting operators.
  • Quantization of classically time-evolved functions.
  • Calculation of expectation values in coherent states.

Related Experiment Videos

  • Analysis of classical Liouville evolution and Gaussian probability densities.

    • Main Results:

    • A method to quantize classical monomials in bosonic theories.
    • Quantum expectation values expressed via Gaussian smoothing of classical functions.
    • A natural semiclassical expansion for quantum expectation values at short times.
    • A general expression for the Ehrenfest time derived from quantum distribution centroid deviation.

    Conclusions:

    • The proposed quantization scheme offers a direct route to semiclassical expansions.
    • The Ehrenfest time can be related to the difference between quantum and classical trajectories.
    • The method is illustrated by analyzing N-coupled nonlinear oscillators.